Abstract: This paper presents a self-adaptive Newmark method whose parameters are dependent upon the structural dynamic characteristics,and the parameters can be analytically determined based on the conditions of minimizing the numerical dispersion and dissipation.The phase error of the proposed method is exactly zero for linear single degree-of-freedom (DOF) dynamic system.Moreover,the proposed method is the most accurate method among the second order integration methods for multi-DOF system and nonlinear system.Numerical simulations validate the present method and the theoretical results.